OFC2 Realign

I scanned the laser on OFC2 for the first time since yesterday. There were higher order mode peaks on the 775 transmission PD at values higher than previously observed. This is most likely due to the earthquake that occured very near campus. I touched up the input alignment and now have almost no higher order modes seen on the TRANS PD.

Pressing the End Mirror Mount

[Erin, Daniel] 

Last Friday, Daniel and I pressed the end mirror mount to try to get different wavefronts from the mirror. The three 'shapes' the mirror is able to produce are a kind of X, an O, and a + (see the third row of Zernike polynomials below for what they look like). We just tried to produce X and the O, since they are the two most straight foward. 

We first took a starting measurement of the mirror with the Shack-Hartmann sensor. This is just to make sure that pressing the mirror still allows us to return to its original state after (it should, this was just a precaution). 

To press in the X, the four screws in the back (side facing us when you look at the table) were engaged (turned until they made contact with the mirror), and two screws in the front were. One suggestion was to place a multimeter on the mirror and the screw so that we could determine exaclty when the screw makes contact with the mirror. Unfortunately, since the entire mount is metal, this will cause the multimeter to short, so this probably won't work. Instead we found it was effective to lightly twist the screwdriver, holding it closer to the screw to apply less torque. After the screws were engaged, we turned them about 45 degrees, since 1mD of curvature is supposed to correspond to 5 degrees of turning (according to the COMSOL simulation. Then we took an image with the Shack-Hartmann sensor. 

After that, we disengaged the screws and took another image. Then, in order to press the O, we enaged 4 screws both in the front and in the back and turned each of the screws 360 degrees. 

Then we disengaged and took a final image. One challenge that might come up is adjusting the modes of the mirror without moving it relative to the sensor or changing the tilt. We found we had to adjust the mirror after pressing it cause it could easily get bumped. Analyzing the data is still in progress, I have a way to reconstruct the wavefront, calculate the radius of curvature, and the next step is to find a way to overlay the engaged and disengaged images to see how the Shack-Hartmann data changes between them. 

Updates on probe signal

[Briana, Ian]

Wiggles in probe scan:

The wiggles tend to be about 0.4 mV in amplitude and a frequency of 4.6 Hz, as seen here. When we are not applying any modulation frequency or temperature scan, we see some variation in power because of the issue with the polarization-maintaining fiber, as seen here. On shorter timescales (zoom in a bunch), there is an additional ~60Hz oscillation, which is apparent whether you're scanning temperature or not. I think the wiggles have been there all along but were just less obvious when I zoomed into the main peak or zoomed out on the power scale. 

My best guess right now is that the power fluctuations are interfering with the scan features in the scanning signal. 

Things that don't affect the squiggles: decreasing the current, moving the fiber, scanning manually. Changing the scan frequency by a factor of two also decreases the frequency of this wiggle by approxiately a factor of 2 as well. Amplitude remains relatively unchanged. mod_200_20240812_174825_Screenshot.png

However, by tuning the modulation frequency/phase, you can suppress some of the oscillations in the error signal and also reach zero offset. If you choose a high modulation frequency, as seen here, the wiggles become much more obvious in the error signal. Based on my zooming, the wiggles' effect on the actual asymmetric error signal don't seem to be that significant, although it's still not ideal for them to exist. 

Why is the error signal offset?

The error signal, when locked, is not at 0 Volts, it is some offset away as seen in this image (purple is error signal, red is photodetector): offsetafterlock_20240812_182448_Screenshot.png. I think what's going on is because the zero-crossing point is offset from the minimum of the peak, the systems locks (see errorsignaloffset.png) to where the error signal intersects the absorption dip minimum. At error signal = 0, the temperature is detuned from the absorption, so the error signal needs to be at an offset. 

Other:

Optimized PID controls of the vapor cell, which you can do automatically by going into Menu -> Ch 1 PID controller -> Auto-tune. Now, the temperature varies at most by 0.05 Celsius in comparison to the 0.5 Celsius oscillations before. This did not fix the wiggles. 

I locked with just the probe at an integrator unity gain frequency of 7.029 Hz and an integrator saturation level of 6.0 dB. After being enlightened about the matplotlib PSD function, this may be the ideal way to get the power spectrum since the Moku is limited at lower frequencies. We took data with a sample acquitsition frequency of 5 kSa/sec for 20 seconds when the laser was locked and not locked. Then, we get the PSD with the following parameters which follows a good averaging method (Welch method): detrend = linear to remove any linear shape in the segments of the power spectrum, Hanning window which is most widely used for making the signal as periodic as possible, NFFT = 256 for standard number of frequency points in the FFT. 

Lee suggested bit noise from the Moku may explain the previous noise spectra. We want to minimize quantization steps in the digitization process (converting the voltage reading to a digital value), so to do this we want to increase the analog signal as much as possible. Increasing the gain on the signal would accomplish this even though the gain amplifies other signal noise. I have not figure out how to increase the gain of the error signal because it might not be possible to increase the gain at a probe point in the laser lock box in the Moku. You could add in the lock-in amplifier but it's a hassle for tuning parameters. Amplifying just the input signal has not proven successful for increasing the error signal. For now, I've taken data with DC at different impedances, which should give an "estimate" for the different gains. The PSDs are shown here: 50_Ohm_impedance_comparison.png, 1_MOhm_impedance_comparison.png. At a higher "gain" (in this case, 1 MOhm impedance means the divider effect is closer to 1 compared to the 50 Ohm impedence which would divide out the signal by some factor less than 1), we would expect more noise so this matches well with the 1 MOhm vs. 50 Ohm PSD comparison. There seems to be no distinction between the locked and unlocked case at either impedance and artifacts in the 50 Ohm one that are not present in the 1 MOhm, not sure why but will retake data tomorrow to make sure it was not some silly mistake. 

KJL Boxes for GQuEST moved to B111B

I moved the KJL Boxes for GQuEST to B111B. I didn't move other components like Thorlabs mounts or screws.

The boxes on the shelves and/or on other boxes are fairly light.

Light fixture above moveable cleanroom in B111B detached

We have detached the light fixture that was blocking the movement of the east moveable cleanroom enclosure in B111B.

The wires that suspend these lights are attached to metal brackets that are screwed into the light casing. Once the screws are removed, the brackets can be removed by prying them out of the plastic casing with a screwdriver. This releases the light, apart from the electrical connection to the ceiling. The electrical wire from the ceiling connects to the wiring inside the light with wire nuts, and cannot easily be detached.  

We released the light fixture from its suspension wires, and rested it on top of the moveable cleanroom. We then moved the cleanroom to adjoin the other one. The electrical wire is long enough to allow some movement of the cleanroom with the light resting on top of it, but we should not try moving the cleanroom more than ~30 cm or so without supporting the light.

Pump path exists and is doing something

Aligned pump. It is easier to align the probe before the pump. Upon scanning, we get the following signals (red is the photodetector signal, blue is the error signal): errsignal_bothpeaks_20240810_132203_Screenshot.png. You can see that the main dip has a peak in the middle (expected by the pump) although it is accompanied by some other weird peaks. The background while scanning is extremely noisy, which could  contribute to these peaks/oscillations in the dip. Additionally, the smaller transition (on the right) now has some extruding peak. A clearer view of the main peak is shown here where we are scanning across temperature: pumpprobe_20240810_130408_Screenshot.png. 

The error signal does not appear to be asymmetric. However, If you change the phase and modulation frequency, it begins to look a bit different and more asymmetric (contrast between differrsignal.png and errsignal_20240810_132122_Screenshot.png). 

One issue is the bumps when scanning temperature, which are apparent in the probe and pump. They are especially obvious when we just measure the probe (blocking the pump), as shown in probe_20240810_125659_Screenshot.png). These tiny wiggles are going to appear in the error signal so we need to find a way to remove them. 

Setup: IMG_2425.jpg

Continued: weird noise spectrum

[Briana, Ian, Torrey]

In my previous post(s), I was taking the noise spectrum of the photodetector signal. I should be taking the noise spectrum of the error signal because 1). the error signal tells you how much the laser is actually drifted and 2). the photodetector signal includes additional effects from the EOM modulation.

Controller

The reason why there is no distinction of noise between the unlocked/locked case at high frequencies is that we are controlling the laser frequency by changing temperature, which is a slow actuator. If we can apply the fast controller to an EOM, we can adjust the frequency of the laser through this phase modulation, adding a fast actuator to our slow (temperature) actuator. Also, there is tradeoff with the gain of the controller. If the gain is too high, your system will be stabilized but there will be a lot of noise. If the gain is too low, then your controller won't be doing anything. Essentially, the gain parameters need to be just right so that the noise spectrum doesn't become amplified. Although useful for stabilization, we are not using the derivative control at all in the slow PID controller because this is a rapidly changing system, so we want the controller to be responsive to those changes. 

Unfortunate noise spectra

At low frequencies, the noise from the locked laser is lower than that from the not locked. At higher frequencies, the locked laser is noisier than the not locked laser. However, I would expect that because of the higher RMS and standard deviation of the error signal when unlocked, the noise should be higher for the unlocked, so it is not clear to me why it is behaving like this. This has been the case for different controllers at unity gain frequencies from 3 Hz to a few hundred Hz. An example of this is using locked5 data (see Nextcloud Users/briana/8_9_2024: LockedUnlockedNoiseSpectra.png with the following controller.

I took data for locked/not locked with a ~3 Hz integrator unity gain frequency and low ~2 dB integrator saturation level (data in NextCloud Users/briana/8_10_2024/noise spectrum probe test). The phasemeter and spectrum analyzer PSD disagree in which situation has the highest noise, although they are in different units. I have not found how the phasemeter converts to Hz/sqrt(Hz), so this could be a reason for the diagreement. Also, I am now again doubtful of the expected order of magnitude of the frequency noise spectrum after looking at the phasemeter ASD. 

Should we use the phasemeter? According to Liquid Instruments, the phasemeter measures frequencies around some acquisition frequency and uses a feedback loop to determine the phase of the input. The signal passes through a mixer and lowpass filter but the signal is mixed with some oscillator. This feedback loop tries to minimize the difference between the input and output frequency, which allows it to determine the frequency/phase. Another oscillator allows it to measure the amplitude. The phasemeter operates on a phase-locked loop, meaning you try to keep the phase of the output constant compared to the phase of the input. Because of this, you need to ensure a phase lock can occur (steady input signal needed), which is more difficult at low frequencies. So, this may not be the optimal instrument for measuring this signal since it relies on a lock and our signal only is affected at low frequencies.

I am going to do a more systematic test of the controller parameters (different gains, unity gain frequencies). I was previously just playing around with values but not documenting the controller well. I will also start taking unlocked laser noise spectra far from resonance to see if the way I'm taking data is causing this phenomenon.

Potential reasons for why locked noise spectrum has more noise?

• Controller issue (feedback gain is too high). I wonder if the shifting polarization of the laser is an issue because that introduces intensity noise, which may start dominating even more with the feedback.

• As Torrey pointed out, it could be that there is more noise with the lock because of shot noise (at the absorption dip, you have less photons so shot noise should increase). 

• Asymmetry of the error signal shouldn't matter because we just care about the linear region. Can the offset of the error signal from zero be an issue? Changing the modulation frequency (not phase shift) shifts the error signal up to avoid offset at the cost of error signal maximization. 

• Is it possible for the zero-crossing point to shift? Ian suggested that if the zero crossing point shifts, the frequency discrimination might be lower, especially if the zero crossing point reaches the ends of the linear region. The system is now not sensitive (the error signal is smaller for larger frequency deviation) so it is less good at reducing noise. 

• Mode hopping of laser. Probably not because this would cause sharp changes in the locking/photodetector signal, which is not apparent in our data (article by rp-photonics.com). 

Other

From Thorlabs specs, the EOM should actually be operating between DC and 100 MHz. Somehow, operating at 120 Hz gave the most symmetric and maximized error signal (400 microvolts amplitude), but it is clearly not built to operate at this level. Anyways, the maximized error signal is now at an EOM driving frequency of 48 MHz (200 microvolts in the positive y direction, 150 in the negative y direction).

Isomet amplifier package (and minicircuits)

We got the isomet amplifiers. These are higher efficiency and can be modulated, so you can make intensity stabilization and such. I put one in a chassis with power supply. You could put 2 - 4 of them as a package. Use a switches and headers to allow easily swapping amps or supplies.

The isomet amps have some LIGO docs up at https://dcc.ligo.org/LIGO-T1900049

This chassis setup can/should be used to package the minicircuits amps as well.

Finesse Model of Higher Order Modes in OFCs

I created a finesse model a single cavity then I added all i = m + n higher order modes (HOMs). I then multiplied four of these cavities with varying length and crusher ROCs together to create a single plot of the higher mode leakage through the higher cavities. The HOMs  height was chosen to match the cavity scans that torrey did on OFC1 which roughly showed that the i=1 mode was 1/10th the power of the i=0 modes and the i=2 modes were 1/100th of the i=0 modes. With these HOM amplitudes and the four cavities multiplied together we have a good model of the HOM leakage in the output filter cavities shown in the attachment: multi_cavity_modes.pdf. The model goes up to n+m = 10 HOMs. Since HOMs contribute less and less as they go up in n+m it is not likely that higher HOMs would change these results significantly. The code for this model is stored in the gquest modeling git. The plot shows the bandpass for the signal at 17.6 MHz and the suppression at the carrier frequency of 0 Hz is a little less than 10^24 in power suppression. The only major improvement to this method is to normalize the power correctly. Currently when you add a HOM it decreases the power in the i=0 mode. so as I add more modes the bandpass section stops having a gain of 1. I have temporarily solved that by increasing the power input from 1 W to 1.3 W which seems to normalize correctly. Fixing this in the future could help reduce uncertainty in this plot. Another difference between this and the real experiment is that I have assumed that the HOM distribution and relative power exiting the IFO will match the laser that we are shining into the OFCs for testing. This should still give us a better understanding of of the performance of the cavities and will give us a comparison when we are doing our final cavity scans of all four cavities. We can also use this to change how the four filter cavities are spaced and their ROCs.

OFC1 Power Budget

Attempting a power budget for loss measurement on OFC1. Haven't touched this cavity in a bit so some minor improvements/debugging were necessary:

-Moku 4 has issues with its wifi. I didn't care to debug this if someone else would like to try and fix this. For now I have a work around of plugging an Ethernet in and downloading the moku app to the NUC. Can connect to Moku 4 like this but it is slower than interacting via Ipad.

-Swapped cables so that I scan the laser frequency on moku 4. No error signal is present. Debugging steps: cable for the 1550 EOM is not shorted. Tank circuit for 1550 EOM is not shorted. Its not the cable. Confirmed it is outputting a voltage. The cavity is indeed scanning on the laser, I see transmission peaks. The REFL dips are very small. Improved 1550 alignment by tweaking input mirrors and maximized on REFL PD. REFL dips improved but still not good. Keeping REFL PD DC coupled and locking the cavity the light canceling on REFL is about 3/8s its original value (80 mv -> 30 mv). This is poor compared to the other cavity.

-The error amplitude is 400-600 uVpp. This used to be an order of magnitude higher and I am not sure why yet.

Calibrating the Shack-Hartmann Sensor

[Erin, Daniel]

The goal of today was to calibrate the Shack-Hartmann sensor in order to make sure that we are ready to start pressing the mirror to view higher order modes tomorrow. This meant we wanted to better focus the lens array, so that the points are directly on the center of each microlens (see the Thor Labs setup linked) and align the end mirror mount so that the contribution by the tilt in the Zernike coefficents is as close to 0 as possible. 

To do this, we made a few changes made to the setup:

• Moved the end mirror mount, the quarter wave plate, and the camera closer to the beam splitter to make sure changing the tilt on the 5 axis stage didn't move the beam out of the view of the camera.
• Mounted the MLA to a lens mount and placed it right in front of the CCD camera so that there is about a focal length between the MLA and the sensor. This vastly improved how the images look (see attached images).
• Added an alignment mirror before the camera to better adjust the setup. 

When it came to reducing the tilt, I got as close to zero as I could, which ended up being a coefficent of around 1.8 for the contribution of the x and the y tilt. I plan to try to keep moving around the 5 axis to get it lower. The points on each of the micro lenses are much more distinct now, not like the squares they looked like before. I also made a wavefront map using these coefficents, and it looks similar to the fizeau data, with a small astigmatism on the mirror that we observed before. 

Finally, just for a quick test, I added a f=300mm lens in front of the mirror to see what would happen and to simulate a curavture. The points appear to move closer together, which we would expect, since it is a converging lens that moves each of the points some relative displacement from the centers of the microlenses. 

Get FFT/PSD of a probe point

Previously, Torrey had to divide out the controller from the control signal to get the error signal. You can avoid all that if you just use the built-in math channel on the laser lock box and set it to take an FFT at a probe point. 

Noise spectrum attempt with increasing integrating unity gain frequency

To collect data from three channels, you can use the triggered data logging. Go to the data logger and set Start -> Triggered then click record. It won't start recording until the trigger hits. I set the trigger to come from the temperature scan signal reaching a certain voltage amount (1 mV). This trigger is the same for both data loggers and then you can enable the temperature scan on the laser lock box to start data collection (once it reaches 1 mV). The two data loggers take up two slots on the multi-instrument mode which is not ideal since we may need more ports for other purposes, but this process works for getting data from >2 channels. The trigger channel needs to be an input channel, it cannot be the external trigger channel. See configuration here: multipledataloggers.png. For now, the Moku Go has been put back on the previously electronics table since we don't need it anymore. 

Retook data (error signal, PSDs) just for a clean slate and also with the above settings since we don't have to shift anything anymore. Because we are using the slow controller, we don't have the issue that Torrey had with having to divide out the effect of the controller from the control signal to get error signal. We can just output it directly from the fast controller track (setting the gain to 0 dB so it essentially doesn't do anything).  The measured error signal today is found here: error_signal.png. The magnitudes of the slopes are (V/nm): ~2.40, (V/Hz) ~4.89e-12. 

At low unity gain frequency, there is overlap: low_unity_freq_psd_comparison.png. As a note, there is a peak at 60 Hz, which I would guess is AC line noise. I was able to get the integrator unity gain frequency to 48.83 kHz (with integrator saturation level of +1.0 dB). The way I am verifying that the controller actually is controlling is ensuring that when I close the switch for control, the photodetector signal does not decrease (moving towards the absorption dip minimum) and the error signal increases. This was the case for when I had the 48.83 kHz integrator unity gain frequency, this picture shows when I broke and reconnected the controller: seemslocked.png. At this higher frequency, we would expect the reduction in noise when locked to be lower. This is unfortunately not the case, the two noise spectra essentially overlap: higher_unity_freq_psd_comparison.png. If we plot the difference between the locked/unlocked PSD (really it is an amplitude spectral density based on the units, PSD would be that squared), there is not a significant difference: Difference.png. The reason for different "levels" of spikness in different section of this graph is becauseI took measurements of the power spectra into three sections: 0Hz to 1 kHz, 1 kHz to 100 kHz. 100 kHz to 1 MHz to get sufficient resolution. The controller for hte higher frequency is shown here: controllerconfig.png.

I think the individual frequency spectra makes sense. I think we should not be using differentials (unlike what Torrey had done, see his log post 2/21/2024) because that was converting a bandwidth of some wavelength amount to that same width in frequency. When we convert from the wavelength to frequency axis, we are just converting a singular value of wavelength to frequency (no distances). The order of magnitude should be around 10^6 Hz/sqrt(Hz), not what I originally thought should be 10^-6 Hz/sqrt(Hz). 

If we look at the spectrum of the error signal, it seems like the unlocked error signal has less noise than the locked one: spectrum_error_signal.png. I am not sure if this is extremely concerning because this just shows the amount of noise in the error signal. But wouldn't we care more about the noise in the actual signal (photodetector?), which tells us more about how our plant? I am not sure if this argument makes sense since the error signal is really just a low-pass filtered version of the photodetector signal. 

 

As far as I know, there are 3 ways to produce the noise spectrum: 1). Use the Moku built-in spectrum analyzer, 2). Use the built-in math channel on the laser lock box and set it to take an FFT, 3). Take a timeseries of the photodetector/error signal and then do an FFT in post processing. The three differ in units and potentially in windowing aka ensuring the ends of the measured signal go to zero at the ends (this would be mainly be the case with the spectrum analyzer). I have not been successful in getting all three to agree yet. 

Anyways, the main issue is that the there is no distinction between the noise level of the locked/unlocked spectra seem to overlap, even at higher unity gain bandwidths. Some thoughts:

• Is this some fundamental issue with the lock? Don't think so. I had also thought that the way I was taking data after unlocking the laser (at the same resonant frequency) might be a problem but I can't think of why since once the controller is not connected to the system, the laser would be free-running. 
• Is the temperature controller not sensitive enough for the error signal changes? Highly doubt it because the amplitude of the scan when locked is not 1 mV, tends to be 19 mV ish, so there should be some wiggle room for the temperature controller to adjust accordingly with the error signal. 
• Can intensity noise from the laser be dominating (relation to the polarizing maintaining fiber causing power to change)? The timescale seems too short for this to happen. Also, is the calibration using the slope canceling out intensity noise? Don't think so.

On the bright side we should be able to lock at higher frequencies than before. Couldn't get the fast controller to lock, will try tomorrow.

OFC2 Power Budget

- Performing 1550 finesse ringdown measurements first. The frequency that matches the two wavelengths has changed. The new frequency that matches them is 232.57 MHz. This is a significant drift in a 24 hour time frame.

-See attached finesse measurements. 1550ringdown.png On one trial (I took more but haven't calculated from them yet) the 1550 finesse is 2486. This is consistant with the previous cavity measurements in transmission.

 

On to the power budget:

-1550nm input: 12.85 mW

-1550nm REFL: 5.9 mW - This measurement is a little tricky. The has a large dependence on how well the AOM frequency is tuned. I held the power meter in the REFL spot and had brianna scan around on the aom frequency to minimize the amount read on the power meter. 

-1550nm TRANS: 2.17 mW - Again, this requires placing the power meter and tuning the frequency to maximize the transmission value.

I don't think 1 - (5.9+2.17) / 12.85 = 37%  worth of loss in this cavity.

 

-775nm input: 76 uW - note the room lights emit a fair amount of 775 light so this is done in the dark.

-775nm REFL: 75 uW make it to the REFL PD - since I can't measure the REFL power while the cavity is locked 11C98CCB-B9ED-4A2E-BF63-3207EF7A87AF.png shows the voltage value on the PD while locked. The max value is roughly 95 mV. This means nearly all the light is cancelling - (2.6 mV (dark voltage) + .8 mV )/ (2.6 mV (dark voltage) + 95 mV ) = 3% the original value. Therefore I'm inferring a power reading of 2.5 uW in reflection.

-775nm TRANS: 22 uW - after a BSW29 (50:50)

I don't think (22*2+2.5)/76 = 38% is the correct loss value. 

 

Update Below:

I went to retry the 775 nm power measurement. I found some very high frequency oscillations in the trans signal due to the controller UGF being too high. Almost a pure sign wave. Because of this the average power the power meter is measuring is way off. This is most likely the case for the 1550 light too, will retry this tomorrow. In the mean time the new measurements are:

Input and REFL - same

TRANS - transmitted on 50:50 BS - 30.7 uW

             - reflected on 50:50 BS - 36 uW

Total exiting the cavity: 66.7 uW (BSW29 on thorlabs quoted up to 1% loss or T_abs + R_abs > 99%, add 1% to this) -> 67.4 uW

This is much closer to the ringdown measurements. Tomorrow I may destroy the 775 TRANS alignment so i can measure without the BS there. And redo the 1550 measurements with this discovery in mind.

 

Initial Frequency Noise Spectrum Attempt

[Briana, Ian]

On 8/5, we took data of the error signal. It is not possible to export the exact error signal you lock to since lock assist mode doesn't have this feature. Because we need 3 channels to be exported, we attached the temperature and photodetector output to the Moku Go, took readings of the error signal and photodetector output with the Moku Pro, and shifted the two so they overlapped in time. Then, the temperature scan, photodetector signal, and error signal could match up reasonably well and we could calibrate the time axis to wavelength. The temperature scan signal is noisy so I fit a line to it when calibrating because the calibration becomes messed up from the noise. Once this is done, we take the linear portion of the error signal (shown in orange in the following plot: error_signal_wavelength.png) and determine the slope (since it passes through the zero point). For the wavelength x-axis error signal, the slope is -1.976 V/nm (makes sense with the error signal: if I get an error signal of 0.002 V, I am detuned ~0.001 nm from resonance). The same can be done when we convert wavelength to frequency, which should technically be easy (f = c/wavelength) except it causes problems in the noise spectrum as I will explain later: error_signal_frequency.png. For the frequency converted x-axis error signal, the slope is 4.19 e-12 V/Hz. This is all under the assumption that the error signal generally has the same shape/slope in the linear region across scans. 

On 8/6, we took the power spectral density plots when the laser is locked and unlocked using the spectrum analyzer. The PSD was taken in two chunks with averaging over 6 samples because at lower frequencies (longer wavelengths), DC noise begins to broaden the spectrum (more room for error in the location of zero points of the wave during detection) so we had to zoom in from 0-100 Hz to get better resolution. Also, with the slow controller, we have a bandwidth of about 3 Hz (anything above will prevent the laser from locking, signal starts oscillating rapidly), which is not great. We took a PSD ranging from 0-10 kHz to cover the controller band. We want to increase the bandwidth (I frequency) of the slow controller so we can get a proper noise spectrum that is less cluttered by DC noise. 

If we just look at these PSDs, we have no metric for how the different voltage ("power") readings correspond to frequency drifts (the y-axis aka power in V/sqrt(Hz) tells us the noise amplitude per frequency bin, but we don't have a good understanding of what this voltage means in terms of noise). So, we use the slope of our error signal to convert the voltage into frequency units (e.g. Hz/sqrt(Hz)), which gives us frequency noise (the linear region passes through the zero crossing point of resonance so we just need the slope as the "linear equation" in terms of detuning is slope * delta_wavelength, where delta_wavelength is the distance from resonance). We use the linear region because beyond the two "peaks," the controller will continuously push the laser frequency away from resonance (in the linear region the slope at the same error signal value would have the opposite derivative compared to the value outside of the peaks, so it pushes the frequency towards resonance instead of away). 

To convert this PSD spectrum to a frequency noise spectrum, we multiply the original power value (V/sqrt(Hz)) by the inverse of slope. The frequency noise spectrum with y-axis in nm/sqrt(Hz) is here: Noise_Spectrum_wavelength.png. There is some distinction between the locked and unlocked case at the lower frequencies but this could also be because of noise fluctuations. On the bright side, the locked case has kind of lower noise. We would benefit from moving to higher frequencies in the controller, I'm still not entirely sure how to do this. The noise spectrum with the power axis in Hz/sqrt(Hz) is here: Noise_Spectrum_frequency.png. The order of magnitude for the frequency spectrum is definitely wrong but I have been unable to find the error so far because the slope from the error signal along with the conversion from wavelength to frequency makes sense to me (getting 0.002 V from the error signal means the frequency is detuned from resonance by ~10^12 Hz, for reference the frequency at 780 nm is around 3.8*10^14 Hz). If anything, there may be a differential (df/dlambda) involved because we are dealing with power, but I don't see a reason why f = c/wavelength shouldn't work. Anyways, I would trust the noise spectrum using wavelength for now. As a note, we used the slopes of the 8/5 error signals to convert from V/sqrt(Hz) to nm/sqrt(Hz). In the future, it will be better to use the error signal from the same measurement time as PSDs. There is a lot of systematic error here but we currently want a rough order of magnitude noise spectrum that makes sense. 

One sanity check for the error signal is that we expect the unlocked scenario to drift more in frequency. When we look at the standard deviation of both error signals (unlocked and locked) using 8/5 data, convert the error signal voltage to a frequency away from the zero point, we get approximately 1.27 MHz for the locked case and 2.76 MHz for the unlocked case. This intuitively makes sense that the error signal would show that the laser has more deviation from the zero point (resonance) when not locked. 

When I refer to unlocked, it means that after we have locked the laser, we break the connection between the controller and temperature scan and let the system do its thing at the fixed temperature at which resonance occurs.

Other notes/things to check tomorrow:

• Current setup: pump path is not really aligned but we will finish measurements before working on that. IMG_2405.jpg
• Triggering data logging could be the way to collect data from three channels: New in Moku v3.1.1: Triggered data logging start acquisition (liquidinstruments.com). Would mean we don't need the Moku Go but haven't figured out how to work this yet. 
• Why can't we use the Phasemeter? Did we take PSDs of the error signal or photodetector signal?
• I also had attempted to create the PSD from taking the Fourier transform of the error signal. The resolution is not great in the region we need (0-100 Hz) but I'd like to try this method again because technically I should get the same result as the spectrum analyzer (I'm not). 

Transposed Direct Form Filter Noise Quantization

Continuing our studies on lowering bit precision, we turn our attention to the transposed version of the direct form filter. This is motivated by our desire to understand how different forms of the biquad filter perform under lower bit resolution, with specific attention to the system's response to noise. I have attached the same plot multiple times, each with different bit resolutions toggled off to highlight the behavior of particular curves. These plots are for a low-pass filter with a 10 MHz sampling frequency, a 10 kHz critical frequency, and an input tone of 12 kHz. For 15 to 35 bits, the digitization and readout noise remain unaffected, and there is also a similar overlay between 10 and 15 bits for higher frequencies. The interesting behavior to note is that when we reduce the resolution from 15 to 10 bits, we observe a counterintuitive decrease in noise level. Reasons for this behavior are unclear. However, 15 bits should be sufficient since increasing bit resolution beyond this does not decrease the noise level.